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<p>In this paper, we solve a three-dimensional partial differential equation using the Hermite wavelet. The Hermite wavelet collocation technique is applied to address the 3D Helmholtz and Poisson equations. The proposed method is straightforward to implement and results in a system of algebraic equations that can be easily solved. We have conducted a detailed error analysis to ensure the reliability of the method. To demonstrate its efficiency and accuracy, we solve two examples each of the Helmholtz and Poisson equations. Additionally, we compare the maximum absolute errors with existing methods in the literature, further validating the robustness of our approach.</p>

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An effective Hermite wavelet collocation method for 3D partial differential equations with convergence analysis

  • 期刊论文

  • 发表日期：

    2025年2月26日

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  • Akmal Raza,
  • Mohammad Prawesh Alam,
  • Mo Faheem

摘要

In this paper, we solve a three-dimensional partial differential equation using the Hermite wavelet. The Hermite wavelet collocation technique is applied to address the 3D Helmholtz and Poisson equations. The proposed method is straightforward to implement and results in a system of algebraic equations that can be easily solved. We have conducted a detailed error analysis to ensure the reliability of the method. To demonstrate its efficiency and accuracy, we solve two examples each of the Helmholtz and Poisson equations. Additionally, we compare the maximum absolute errors with existing methods in the literature, further validating the robustness of our approach.